Tackling complex models in systems biology

One of the main obstacles in systems biology is complexity, a feature that is inherent to living systems. This complexity stems both from the large number of components involved and from the intricate interactions between these components. When the system is described by a mathematical model, we frequently end up with a large nonlinear set of mathematical equation that contains many parameters. Such a large model usually has a number of undesirable properties, e.g., its dynamical behavior is hard to understand, its parameters are difficult to identify, and its simulation requires a very long computing time. In this thesis, we present several strategies that may help to overcome these problems. On the level of method development, we focus on two issues: a) method development to analyze robustness, and b) method development to reduce model complexity. On the level of practical systems biology, we develop and analyze a model for the cell cycle in tomato fruit pericarp.

 

Robustness, that is the ability of a system to preserve biological functionality in spite of internal and external perturbations, is an essential feature of a biological system. Any mathematical model that describes this system should reflect this property. This implies the needs of a mathematical method to evaluate the robustness of mathematical models for biological processes. However, assessing robustness of a complex non-linear model that contains many parameters is not straightforward. In this thesis, we present a novel method to evaluate the robustness of mathematical models efficiently. This method enables us to find which parameter combinations in a model are responsible for its robustness. In this way, we get more insight into the underlying mechanisms that govern the robustness of the biological system. The advantage of our method is that the effort to apply the method scales linearly with the number of parameters. It is therefore very efficient when it is applied on mathematical models that contain a large number of parameters.

 

The complexity in a model can be brought down by simplifying the model. In this thesis, we also present a novel reduction method to simplify mathematical representations of biological models. In this method, biological components and parameters that do not contribute to the observed dynamics are considered redundant and hence are removed from the model. This results in a simpler model with less components and parameters, without losing predictive capabilities for any testable experimental condition. Since the reduced model contains less parameters, parameter identification can be carried out more efficaciously.

 

In the last part of this thesis we show how modeling can help us in understanding the cell cycle in tomato fruit pericarp. The cell cycle in this system is quite unique since the classical cell cycle, in which the cell division takes place, after some periods turns into a partial cycle where the cell keeps replicating its DNA but skips the division. Several mechanisms that are putatively responsible for this transition have been proposed. With modeling, we show that although each of these putative mechanisms could lead on its own the cell cycle to this transition, also their combination could lead to the same result. We also show that the mechanisms that yield the transition are very robust.